If a radioactive isotope has a half life of 162 days how many half lives would it need to go through to have 50% of that isotope to be non-radioactive?
162 days if none of the products are radioactive.
Half life means half is gone.
Do not cheat plz!
To determine the number of half-lives required for a radioactive isotope to reach 50% of its initial amount, you can use the formula:
N = Nā * (1/2)^(t / T)
Where:
N is the remaining fraction of the isotope
Nā is the initial fraction of the isotope (in this case, 1, since we're starting with 100%)
t is the time passed
T is the half-life of the isotope
In this case, we want to find out how many half-lives it takes for the remaining fraction (N) to reach 50%, or 0.5.
0.5 = 1 * (1/2)^(t / 162)
To solve for t, we can take the logarithm of both sides:
log(0.5) = log((1/2)^(t / 162))
Using the logarithmic property log(x^y) = y * log(x):
-0.301 = (t / 162) * log(1/2)
Now, we can solve for t by multiplying both sides by 162 and dividing by log(1/2):
t = -0.301 * 162 / log(1/2)
Using a calculator, we find that t ā 109.98.
Since the number of half-lives must be a whole number, we can round t up to the nearest whole number, resulting in approximately 110 half-lives.
Therefore, it would take approximately 110 half-lives for 50% of the radioactive isotope to become non-radioactive.